Algebra Examples

$\frac{36 m^{4} y^{4} - 18 m^{3} y^{2}}{6 m^{2} y}$

Step 1

Factor $18 m^{3} y^{2}$ out of $36 m^{4} y^{4} - 18 m^{3} y^{2}$ .

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Step 1.1

Factor $18 m^{3} y^{2}$ out of $36 m^{4} y^{4}$ .

$\frac{18 m^{3} y^{2} (2 m y^{2}) - 18 m^{3} y^{2}}{6 m^{2} y}$

Step 1.2

Factor $18 m^{3} y^{2}$ out of $- 18 m^{3} y^{2}$ .

$\frac{18 m^{3} y^{2} (2 m y^{2}) + 18 m^{3} y^{2} (- 1)}{6 m^{2} y}$

Step 1.3

Factor $18 m^{3} y^{2}$ out of $18 m^{3} y^{2} (2 m y^{2}) + 18 m^{3} y^{2} (- 1)$ .

$\frac{18 m^{3} y^{2} (2 m y^{2} - 1)}{6 m^{2} y}$

Step 2

Cancel the common factor of $18$ and $6$ .

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Step 2.1

Factor $6$ out of $18 m^{3} y^{2} (2 m y^{2} - 1)$ .

$\frac{6 (3 m^{3} y^{2} (2 m y^{2} - 1))}{6 m^{2} y}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $6$ out of $6 m^{2} y$ .

$\frac{6 (3 m^{3} y^{2} (2 m y^{2} - 1))}{6 (m^{2} y)}$

Step 2.2.2

Cancel the common factor.

$\frac{6 (3 m^{3} y^{2} (2 m y^{2} - 1))}{6 (m^{2} y)}$

Step 2.2.3

Rewrite the expression.

$\frac{3 m^{3} y^{2} (2 m y^{2} - 1)}{m^{2} y}$

Step 3

Cancel the common factor of $m^{3}$ and $m^{2}$ .

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Step 3.1

Factor $m^{2}$ out of $3 m^{3} y^{2} (2 m y^{2} - 1)$ .

$\frac{m^{2} (3 m y^{2} (2 m y^{2} - 1))}{m^{2} y}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $m^{2}$ out of $m^{2} y$ .

$\frac{m^{2} (3 m y^{2} (2 m y^{2} - 1))}{m^{2} (y)}$

Step 3.2.2

Cancel the common factor.

$\frac{m^{2} (3 m y^{2} (2 m y^{2} - 1))}{m^{2} y}$

Step 3.2.3

Rewrite the expression.

$\frac{3 m y^{2} (2 m y^{2} - 1)}{y}$

Step 4

Cancel the common factor of $y^{2}$ and $y$ .

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Step 4.1

Factor $y$ out of $3 m y^{2} (2 m y^{2} - 1)$ .

$\frac{y (3 m y (2 m y^{2} - 1))}{y}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Raise $y$ to the power of $1$ .

$\frac{y (3 m y (2 m y^{2} - 1))}{y^{1}}$

Step 4.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (3 m y (2 m y^{2} - 1))}{y \cdot 1}$

Step 4.2.3

Cancel the common factor.

$\frac{y (3 m y (2 m y^{2} - 1))}{y \cdot 1}$

Step 4.2.4

Rewrite the expression.

$\frac{3 m y (2 m y^{2} - 1)}{1}$

Step 4.2.5

Divide $3 m y (2 m y^{2} - 1)$ by $1$ .

$3 m y (2 m y^{2} - 1)$

Step 5

Apply the distributive property.

$3 m y (2 m y^{2}) + 3 m y \cdot - 1$

Step 6

Multiply $m$ by $m$ by adding the exponents.

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Step 6.1

Move $m$ .

$3 (m \cdot m) y (2 y^{2}) + 3 m y \cdot - 1$

Step 6.2

Multiply $m$ by $m$ .

$3 m^{2} y (2 y^{2}) + 3 m y \cdot - 1$

Step 7

Multiply $- 1$ by $3$ .

$3 m^{2} y (2 y^{2}) - 3 m y$

Step 8

Simplify each term.

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Step 8.1

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 8.1.1

Move $y^{2}$ .

$3 m^{2} (y^{2} y) \cdot 2 - 3 m y$

Step 8.1.2

Multiply $y^{2}$ by $y$ .

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Step 8.1.2.1

Raise $y$ to the power of $1$ .

$3 m^{2} (y^{2} y^{1}) \cdot 2 - 3 m y$

Step 8.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 m^{2} y^{2 + 1} \cdot 2 - 3 m y$

Step 8.1.3

Add $2$ and $1$ .

$3 m^{2} y^{3} \cdot 2 - 3 m y$

Step 8.2

Multiply $2$ by $3$ .

$6 m^{2} y^{3} - 3 m y$